# Multiplying Mixed Numbers

## Multiplying Mixed Numbers - How it Works - Video

### Example 1 Example 1:

When multiplying mixed numbers, we need to to convert the mixed numbers into improper fractions. So we need to multiply the denominator and the whole number and add the numerator and keep the denominator. So 2 and 1/3 becomes 7/3 because 3 x 2 + 1 = 6 + 1 = 7. And 1 and 3/5 becomes 8/5. Now, we have the fractions 7/3 and 8/5. So we multiply the numerators, 7 x 8 = 56 and then the denominators, 3 x 5 = 15. The result is 56/15. Now we have to use long division to find our mixed number. 56/15 is 3 remainder 11. So our final result is 3 and 11/15.

### Example 2 Example 2:

When multiplying mixed numbers, we need to to convert the mixed numbers into improper fractions. So we need to multiply the denominator and the whole number and add the numerator and keep the denominator. So 3 and 1/4 becomes 13/4 because 4 x 3 + 1 = 12 + 1 = 13. And 1 and 2/3 becomes 5/3. Now, we have the fractions 13/4 and 5/3. So we multiply the numerators, 13 x 5 = 65 and then the denominators, 4 x 3 = 12. The result is 65/12. Now we have to use long division to find our mixed number. 65/12 is 5 remainder 5. So our final result is 5 and 5/12.

### Example 3a Example 3a:

When multiplying mixed numbers, we need to to convert the mixed numbers into improper fractions. So we need to multiply the denominator and the whole number and add the numerator and keep the denominator. So 2 and 1/2 becomes 5/2 because 2 x 2 + 1 = 4 + 1 = 5. And 1 and 4/5 becomes 9/5. Now, we have the fractions 5/2 and 9/5. So we multiply the numerators, 5 x 9 = 45 and then the denominators, 6 x 5 = 30. The result is 45/30. Now we have to use long division to find our mixed number. 45/30 is 1 remainder 15. Now we have 1 and 15/30. But we are not done yet, we have to reduce 15/30 to 1/2. So our final result is 1 and 1/2.

### Example 3b Example 3b:

When multiplying mixed numbers, we need to to convert the mixed numbers into improper fractions. So we need to multiply the denominator and the whole number and add the numerator and keep the denominator. So 2 and 1/2 becomes 5/2 because 2 x 2 + 1 = 4 + 1 = 5. And 1 and 4/5 becomes 9/5. Now, we have the fractions 5/2 and 9/5.

This time we are going to reduce the numbers so we can make the numbers smaller. Everybody loves smaller numbers. Now we can simplify the 5 in the numerator because there is a 5 in the denominator. So we can divide 5 ÷ 5 = 1 to get smaller numbers. Next we can do 9 ÷ 3 = 3 and 6 ÷ 3 = 2 since 9 and 6 are multiples of 3. Now we have 1 x 3 on top and 2 x 1 on the bottom and that is 3/2. Using long division, we get 1 remainder. So our final result is 1 and 1/2.

The same as 3a.

### Example 4 Example 4:

When multiplying mixed numbers, we need to to convert the mixed numbers into improper fractions. So we need to multiply the denominator and the whole number and add the numerator and keep the denominator. So 4 and 2/3 becomes 14/3 because 3 x 4 + 2 = 12 + 2 = 14. And 5 and 5/8 becomes 45/8. Now, we have the fractions 14/3 and 45/8.

This time we are going to reduce before we multiply the top and bottom. Everybody loves smaller numbers. Now we can simplify the 45 and the 3 because both are multiples of 3. So, we divide 45 ÷ 3 = 15 and 3 ÷ 3 = 1. Now we can simplify the 14 and 8 because they are multiples of 2. So, 14 ÷ 2 = 7 and 8 ÷ 2 = 4. So now we have 7 x 15 on top and 1 x 4 on the bottom, which is 105/4. After we use long division to find the mixed number, our answer is 26 and 1/4.

## Live Worksheet

Here is the link if you prefer.